Almost every aspect of life in the twenty-first century involves the use of electric power. However, most users of electricity do not realize that, before electricity reaches their premises, it travels through a complex network of electric power generation and distribution systems. The complexity of power generation and distribution is frequently underscored by blackouts, such as those that occurred over most of the northeastern United States and Canada on Aug. 14 and 15, 2003, which make it clear that the various processes and systems involved in the generation and the distribution of electricity require very careful planning.
In the United States, electric power generation and distribution was traditionally highly regulated by federal government agencies, such as the Federal Energy Regulatory Committee (FERC), as well as by utility commissioners of various states. These regulating bodies set performance standards and requirements for the generation and the distribution of electric power for the utility companies (hereinafter referred to as “utilities”) which generated and distributed electric power. For example, these regulating bodies specified the requirements for real power at various points on the electric distribution systems. In response to the specified requirements, the utilities determined how much electricity to produce, where to produce it, and how to distribute it.
Utilities generate electricity using various types of power generators, which may be categorized depending on the energy used to generate electricity, into thermal, nuclear, wind, hydroelectric, etc., generators. Each of these various types of generators operates under different sets of constraints. For example, an output of a thermal generator is a function of the heat generated in a boiler, wherein the heat generated per hour is constrained by the amount of fuel that can be burned per hour.
Once the utilities received the requirements for real power to be delivered, the utilities determined which generation unit to use at what level. In making this determination, the utilities took into consideration the constraints on each of the available power generators. Moreover, to minimize the cost of power generation, the utilities typically tried to find the optimum combination of power generation using any of a number of sophisticated mathematical and forecasting models available for planning the generation of electricity. Specifically, computer programs generally known as economic dispatch programs were available to help utilities make decisions related to the operation of electric generators based on real power requirements.
As is well known, electric power includes both real power, which is given in megawatts (MWs), and reactive power, which is given in mega volt-amperes reactive (MVARs). Because, utilities traditionally received requirements for electric power in real power only, traditional economic dispatch programs determined optimum operating solutions only in terms of real power. As a result, these programs allowed utilities to determine optimal operation of various generators based on a specified real power, but did not take into account the reactive power requirement. However, it is necessary to keep a certain level of reactive power on the electric distribution grids to avoid damage to transformers and other electrical distribution equipments. As a result, utilities still have to generate and distribute at least some reactive power.
The behavior of generators with respect to the generation of reactive power is provided by the so called reactive capability curves of the generators. The reactive capability curves are a graphical representation of the reactive and real power produced by the generators under various operating conditions, as specified by the cold gas pressure and cold gas temperature inside the generators as well as the power factor of the generated electric power. Manufacturers of the generators provide the estimated reactive capability curves to the operators of the generators. However, as generators are used, over time the actual reactive capability curves of the generators would deviate from the estimated reactive capability curves. Therefore, it is necessary to provide a method to determine updated reactive capability curves that may be used by an economic dispatch program used by the power plants.